Issue |
ESAIM: COCV
Volume 25, 2019
|
|
---|---|---|
Article Number | 21 | |
Number of page(s) | 20 | |
DOI | https://doi.org/10.1051/cocv/2018014 | |
Published online | 23 July 2019 |
Existence for dislocation-free finite plasticity
1
Faculty of Mathematics, University of Vienna,
Oskar-Morgenstern-Platz 1,
1090
Wien, Austria
2
Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes,
v. Ferrata 1,
27100
Pavia, Italy
* Corresponding author: ulisse.stefanelli@univie.ac.at
Received:
9
October
2017
Accepted:
13
February
2018
This note addresses finite plasticity under the constraint that plastic deformations are compatible. In this case, the total elastoplastic deformation of the medium is decomposed as y = ye ○ yp, where the plastic deformation yp is defined on the fixed reference configuration and the elastic deformation ye is a mapping from the varying intermediate configuration yp(Ω). Correspondingly, the energy of the medium features both Lagrangian (plastic, loads) and not Lagrangian contributions (elastic).
We present a variational formulation of the static elastoplastic problem in this setting and show that a solution is attained in a suitable class of admissible deformations. Possible extensions of the result, especially in the direction of quasistatic evolutions, are also discussed.
Mathematics Subject Classification: 35K90
Key words: Finite plasticity / static problem / existence / quasistatic evolution
© EDP Sciences, SMAI 2019
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